Calculate the freezing point and boiling point of a solution containing 7.55 g of ethylene glycol (C2H6O2) in 85.7 mL of ethanol. Ethanol has a density of 0.789 g/cm³.

Verified step by step guidance

1. Calculate the molality of the solution by first determining the moles of ethylene glycol using its molar mass.
2. Convert the volume of ethanol to mass using its density, then convert this mass to kilograms.
3. Use the formula for molality: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \).
4. Apply the freezing point depression formula: \( \Delta T_f = i \cdot K_f \cdot m \), where \( i \) is the van't Hoff factor (1 for ethylene glycol), and \( K_f \) is the freezing point depression constant for ethanol.
5. Apply the boiling point elevation formula: \( \Delta T_b = i \cdot K_b \cdot m \), where \( K_b \) is the boiling point elevation constant for ethanol.

Key Concepts

Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. These properties include boiling point elevation and freezing point depression, which are crucial for calculating the changes in freezing and boiling points when a solute is added to a solvent.

Molar Mass and Density Calculations

To determine the effects of a solute on the freezing and boiling points, it is essential to calculate the molar mass of the solute and the mass of the solvent. The density of ethanol allows for the conversion of volume (mL) to mass (g), which is necessary for finding the molality of the solution and applying the colligative property formulas.

Freezing Point Depression and Boiling Point Elevation Formulas

The freezing point depression and boiling point elevation can be calculated using the formulas ΔTf = i * Kf * m and ΔTb = i * Kb * m, where ΔT is the change in temperature, i is the van 't Hoff factor, Kf and Kb are the freezing point depression and boiling point elevation constants for the solvent, and m is the molality of the solution. Understanding these formulas is essential for solving the problem at hand.